Swearing, or 'SWORE' in this case, is an act of making a solemn promise or vow. Attesting and attesting to something is a way of providing evidence or testimony that something is true. To ATTEST is to provide evidence or testimony that something is true. Finally, to 'SEE' something is to observe it or be aware of it. All together, to bore witness to something is to swear, ATTEST, and observe something, thereby providing evidence that it is true.